Bayesian analysis in single-index quantile regression with missing observation

Abstract

Based on Bayesian method, we investigate single-index quantile regression with missing observation. In particular, using spline approximation for the link function, we construct quasi-posterior distribution of the index vector based on asymmetric Laplace likelihood with missing observation, and establish asymptotically normality of the posterior estimator of the index parameters. At the same time, we use a hierarchical model based on spike and slab Gaussian priors to do variable selection and study consistency of the variable selection. Finite sample performance of the proposed methods is analyzed via simulation and real data too.

Keywords:

• Asymptotic normality
• Bayesian analysis
• missing at random
• posterior distribution
• single-index quantile regression

2000 Mathematics Subject Classifications:

• 62C10
• 62E20

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (12071348) and National Social Science Foundation of China (17BTJ032).